An iodine molecule dissociates into atom after absorbing light of wavelength `4500`Å. If quantum of radiation is absorbed by each molecule calculate the kinetic energy of iodine (Bond energy of `I_(2)` is `240`` kJ mol^(-1))`

Options

A. `2.16 xx10^(-20)` j
B. `1.88 xx10^(-22) j`
C. ` 3.47 xx10^(-19)` j
D. `5.55 xx 10^(-21)` j

Answer

To solve the problem step by step, we will follow the outlined procedure:

### Step 1: Convert Bond Energy from kJ/mol to J/atom
Given:
- Bond energy of \( I_2 \) = 240 kJ/mol

First, we convert this energy into joules per mole:
\[ \text{Bond energy in J/mol} = 240 \, \text{kJ/mol} \times 1000 \, \text{J/kJ} = 240000 \, \text{J/mol} \]

Next, we convert this to energy per atom using Avogadro's number (\( N_A = 6.022 \times 10^{23} \, \text{mol}^{-1} \)):
\[ \text{Bond energy per atom} = \frac{240000 \, \text{J/mol}}{6.022 \times 10^{23} \, \text{mol}^{-1}} \approx 3.9847 \times 10^{-19} \, \text{J} \]

### Step 2: Calculate the Energy Absorbed from the Light
We use the formula for the energy of a photon:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h = 6.626 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 4500 \, \text{Å} = 4500 \times 10^{-10} \, \text{m} = 4.5 \times 10^{-7} \, \text{m} \)

Now substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{4.5 \times 10^{-7} \, \text{m}} \approx 4.4173 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the Kinetic Energy of Iodine Molecule
The kinetic energy (KE) of the iodine molecule after dissociation can be calculated by subtracting the bond energy from the absorbed energy:
\[ \text{Kinetic Energy} = E_{\text{absorbed}} - E_{\text{bond}} \]
Substituting the values:
\[ \text{Kinetic Energy} = 4.4173 \times 10^{-19} \, \text{J} - 3.9847 \times 10^{-19} \, \text{J} \approx 4.326 \times 10^{-20} \, \text{J} \]

### Step 4: Calculate the Kinetic Energy per Atom
Since the iodine molecule \( I_2 \) consists of two atoms, we divide the kinetic energy by 2:
\[ \text{Kinetic Energy per atom} = \frac{4.326 \times 10^{-20} \, \text{J}}{2} \approx 2.165 \times 10^{-20} \, \text{J} \]

### Final Answer
The kinetic energy of iodine after dissociation is approximately:
\[ \text{Kinetic Energy} \approx 2.165 \times 10^{-20} \, \text{J} \]

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